Clóscríobh is a compound word - Caol le caol agus leathan le leathan doesn't apply across the boundary in compound words. Other examples that you might have encountered are gluaisrothar and mótarbhealach.
The verbal adjective of clóscríobh is clóscríofa. While you will still find the variants scríobhta and scríobhtha used in place of scríofa, that doesn't appear to be the case with clóscríofa - the handful of examples can be written off as either archaic or simple mistakes.
The proposed solution takes "adh" added to the autonomous pronoun. But the notes suggest this is the case for single syllable verbs. Multi-syllable verbs would take "aiodh". Since this is a compound word is there another rule in place?
One of the rules for lenition that I thought I had worked out is that it is used for verbs in the past tense. Why is it not used here? Is the Cló not considered part of the verb, and the rule is only applied to the scríobh part of the word (which wouldn't be lenited anyway)?